Multi-wavelength phase mask

ABSTRACT

Among other aspects, various embodiments include encoding wavelength-based characteristics, in addition to three-dimensional positions, of a plurality of objects of a plurality of different wavelengths directly in an image of the objects.

FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with Government support under contract GM085437awarded by the National Institutes of Health. The Government has certainrights in the invention.

BACKGROUND

Understanding of living cells is beneficial for a variety of researchand development. In order to understand the complex machinery at workwithin living cells, the position of individual biomolecules ismeasured. For example, single-particle tracking (SPT), in which thetrajectory of a moving individual molecular label, quantum dot, ornanoparticle is determined, provides a valuable tool for a wide range ofbiological applications. Information inferred from the extractedparticle trajectory sheds light on physical properties such as particlesize, conformation, and the local environment, because observing themotion of single particles directly unmasks nanoscale behavior such asdiffusion, directed motion, or anisotropy. A useful way to obtaininformation is to label different objects in different colors,increasing the optical complexity of the system.

These and other matters have presented challenges to three-dimensionalimaging of multicolored particles, for a variety of applications.

SUMMARY

The present invention is directed to overcoming various challengesrelated to the types of devices and techniques discussed above and inother implementations. The present invention is exemplified in a numberof implementations and applications, some of which are summarized belowas examples.

Various embodiments in accordance with the present disclosuresimultaneously measure all of these physical parameters, with minimalmodification of a conventional microscope. For example, in someembodiments, a 4 f optical processing circuitry is added to the cameraof the conventional microscope. In other embodiments, prisms or gratingswith wavelength-dependent characteristics are used to create amultiplicity of optical paths. In addition, such apparatus embodimentsincludes a relatively simple and cheap light-sheet microscope.

A number of aspects of the present disclosure include a methodcomprising encoding wavelength-based characteristics, in addition todata concerning or defining three-dimensional positions, of objects of aplurality of different wavelengths directly in an image of the objects.In various specific aspects, the wavelength-based characteristics areencoded (in addition to data concerning the three-dimensionalpositions), of the objects by simultaneously providing a different phasedelay for (each of) the different wavelengths from light passing alongan optical path using a phase mask. In specific aspects,wavelength-based characteristics and three-dimensional positions areencoded for at least two objects, using a single phase mask and withinone field of view, that are labeled using different colors. Each of thedifferent colors corresponds to one of the plurality of wavelengths. Inrelated aspects, the image of the objects is generated by passing lightalong an optical path from the objects to a phase mask, and providing adifferent phase delay, using the phase mask, for each of the differentwavelengths from the light passed along the optical path.

Various aspects of the present disclosure include an apparatuscomprising a phase mask and circuitry. The phase mask is arranged withoptics in an optical path to modify a shape of light for each of aplurality of wavelengths of light passed from a plurality of objects.For example, the shapes of light are modified for each respectivewavelength independently of one another by the phase mask simultaneouslyproviding different phase delays for each wavelength and using a singleoptical channel. The circuitry characterize a three-dimensional image ofthe objects based on each of the modified shapes of light and therespective wavelengths. In specific aspects, the circuitry detectsrelative movement of different ones of the objects based upon themodified shape of lights.

Other related aspects of the present disclosure include a methodcomprising providing optics and a phase mask in an optical path. Lightis passed through the optical path to circuitry where the light isdetectable. Further, circuitry encodes wavelength-based characteristicsof a plurality of objects based on the detected light. For example, thewavelength-based characteristics of the objects are encoded by modifyinga shape of light passing along the optical path for each of a pluralityof wavelengths of light passed from the objects. In various specificaspects, the method further includes concurrently locating the objects,such as particles, in the single optical path based on the modifiedshapes of light for each respective wavelength. For example, the objectsare labeled in different colors and the locations of the objects aretracked based on the encoded wavelength-based characteristics andthree-dimensional positions (x, y, and z).

Various more specific aspects of the present disclosure include anapparatus comprising an imaging circuit, optics, and a phase mask. Theimaging circuit is at an image plane in the optical path for detectinglight at or incident upon the imaging circuit. The optics pass lightfrom the objects toward the image plane. And, the phase mask is arrangedwith the optics to modify a shape of light passing along the opticalpath, passed from the objects. The light passing along the optical pathis modified to create a point-spread-function (PSF) for each of aplurality of respective wavelengths of light passed from the objects andalong the optical path. The circuit characterizes a three-dimensionalimage of the objects based on each of the modified shapes of light andthe respective wavelengths.

Other specific aspects include axial-related and/or 3D-relatedmicroscopic localization of multiple point-like light objects labeled indifferent wavelengths as generated using wide-field microscopy. Inaccordance with various aspects 3D (x, y, and z) position information isobtained, even when an object is above or below the focal plane. Inother aspects, less than all the 3D information is needed; for example,the axial (z) information alone and/or in combination with some lateral(x or y) information is used instead of the full 3D positioninformation.

According to other aspects, the present disclosure is directed to phasemasks that are optimized to create PSFs corresponding to wavelengthsexpected from target objects and/or to the manufacture and/or use ofsuch phase masks. In some embodiments, the phase mask is placed at theFourier plane of the optical system to yield a shift-invariant PSF.

In other related embodiments, the present disclosure is directed to amethod that includes determining a set of different wavelengths orwavelength ranges for defining voltage patterns for phase mask, and thenusing an optimization function to provide an optimal voltage patternapplicable to each of the different wavelengths or wavelength ranges andthereby determining an optimal voltage pattern for a desired singlephase mask. This phase mask is then characterized by the pattern andused to create PSFs that are sufficiently similar to desired phase masksas though respectively manufactured for each of the differentwavelengths or wavelength ranges.

The above discussion/summary is not intended to describe each embodimentor every implementation of the present disclosure. The figures anddetailed description that follow also exemplify various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

Various example embodiments may be more completely understood inconsideration of the following detailed description in connection withthe accompanying drawings, in which:

FIGS. 1A-1B illustrate example apparatuses in accordance with variousembodiments;

FIG. 2 illustrates an example of an apparatus in accordance with variousembodiments;

FIGS. 3A-3B illustrate an example of fluorescent beads imaged using anapparatus, in accordance with various embodiments;

FIG. 4 illustrates an example of a phase mask in accordance with variousembodiments;

FIGS. 5A-5B illustrate an example phase mask and point spread functionsfor different wavelengths created using the phase mask, in accordancewith various embodiments;

FIG. 6 illustrates an example phase mask, in accordance with variousembodiments;

FIGS. 7A-7D illustrate examples of a dual-wavelength phase mask, inaccordance with various embodiments;

FIGS. 8A-8G illustrate a dual-wavelength phase mask and correspondingpoint spread functions for two different wavelengths, in accordance withvarious embodiments;

FIGS. 9A-9D illustrate an example of three dimensional localization oftwo differently labeled objects using a multi-wavelength phase mask, inaccordance with various embodiments;

FIGS. 10A-10C illustrate an example of multi-wavelength super resolutionimaging using a multi-wavelength point spread function, in accordancewith various embodiments;

FIG. 11 illustrates an example 3D rendering of tetrapod PSF, inaccordance with various embodiments; and

FIGS. 12A-12B illustrate examples of a light sheet microscope, inaccordance with various embodiments.

While various embodiments discussed herein are amenable to modificationsand alternative forms, aspects thereof have been shown by way of examplein the drawings and will be described in detail. It should beunderstood, however, that the intention is not to limit the invention tothe particular embodiments described. On the contrary, the intention isto cover all modifications, equivalents, and alternatives falling withinthe scope of the disclosure including aspects defined in the claims. Inaddition, the term “example” as used throughout this application is onlyby way of illustration, and not limitation.

DETAILED DESCRIPTION

Aspects of the present disclosure are believed to be applicable to avariety of different types of apparatuses, systems and methods involvingencoding wavelength-based (e.g., color) characteristics andthree-dimensional positions of a plurality of objects. For example, thewavelength-based characteristics and three-dimensional positions areencoded by modifying respective point-spread-functions (PSFs) for eachwavelength of light passed from the plurality objects via a phase mask.In certain implementations, aspects of the present disclosure have beenshown to be beneficial when used in the context of optical microscopy orwith PSFs that vary based on a depth range. While the present inventionis not necessarily limited to such applications, various aspects of theinvention may be appreciated through a discussion of various examplesusing this context.

Accordingly, in the following description various specific details areset forth to describe specific examples presented herein. It should beapparent to one skilled in the art, however, that one or more otherexamples and/or variations of these examples may be practiced withoutall the specific details given below. In other instances, well knownfeatures have not been described in detail so as not to obscure thedescription of the examples herein. For ease of illustration, the samereference numerals may be used in different diagrams to refer to thesame elements or additional instances of the same element.

For particle tracking and/or three dimensional (3D) imaging, the contextin which the imaging takes place is often of interest. For example, whentracking a moving emitter in a cell, the motion of the emitter relativeto other elements in the cell provides vital information. As anotherexample, a trajectory of a protein, or a structure within a cell, ismore informative when it is related to other proteins, organelles, orthe cell membrane. In order to track the movement of one object relativeto movement of another object, the objects are labeled using differentcolors. For example, one object is labeled in a first wavelength (e.g.,color) and the other object is labeled in a second wavelength that isdifferent than the first wavelength. Certain embodiments in accordancewith the present invention include an apparatus with a phase mask thatmodifies a shape of light for each of a plurality of wavelengths oflight passed from objects. The phase mask modifies the shape of light togenerate a point spread function (PSF). A single phase mask cansimultaneously create different PSFs, one for each wavelength, using asingle optical channel and camera/detector and resulting in an increasedamount of information and increased simplicity obtainable as compared toother techniques. Such other techniques include additional opticalchannels (e.g., multiple cameras), sequential imaging, wavelengthdispersive optics (e.g., gratings, prisms) and/or dedicated fields ofview for each wavelength. For example, for each color being imaged, adedicated optical channel is used. Each dedicated optical channelrequires use of an additional imaging apparatus (e.g., camera) or takesup some of the field of view of a particular imaging apparatus. Further,the imaging apparatus has corresponding special filters or other opticswith wavelength-dependent transmission. However, this limits the numberof different colors that can be used and thus the amount of informationobtainable from the acquired data.

Various embodiments involve super-resolution microscopy.Super-resolution microscopy is a form of light microscopy that allowsimages to be taken with a higher spatial resolution than the opticaldiffraction limit. Surprisingly, a number of embodiments of the presentdisclosure encode spectral information (wavelengths/color) in additionto the 3D position, directly in the image. By exploiting chromaticdispersion, a phase mask simultaneously yields controllably differentPSFs for different wavelengths in a single field of view. Further, invarious embodiments, objects labeled in multiple wavelengths aresimultaneously tracked using super-resolution imaging and a singleoptical path.

In some specific embodiments, aspects of the present disclosure involvelocalization of individual objects that are labeled with differentwavelengths in optical microscopy. For example, a phase mask is added toa conventional microscope. The phase mask includes a dielectric mask,deformable mirror, or a spatial light modulator (SLM), such as a liquidcrystal SLM. A spectral degree of freedom is added to the microscope bymodifying a shape of light detected using a phase mask that is in theFourier plane of the optical path of a microscope. In variousembodiments the phase mask is used to encode thewavelength-characteristics and three-dimensional position of multipleobserved objects (e.g., particles, emissive molecules, scatteringobjects).

The phase mask, in various embodiments, exploits the spectral dependenceof the light corresponding to different objects and creates different,controllable, phase delay patterns (e.g., PSFs) for differentwavelengths. As a result, different wavelengths correspond to differentPSFs. The phase mask is designed with a particular thickness such thatat any point on the phase mask, the mask produces a different phasedelay for respective wavelengths. This occurs by taking advantage of therefractive index change between the mask material (e.g., dielectricmaterial, quartz, deformable air, and liquid-crystal) and air.Accordingly, embodiments in accordance with the present disclosure,involve a single optical channel to simultaneously image multiple,distinguishable objects labeled with different colors and/or objects ofdifferent wavelengths. An object, as used herein, corresponds to and/orincludes an emitter, such as a particle, a molecule, a cell, a quantumdot, a nanoparticle, etc. Further, multi-wavelength spatial registrationis simplified as all wavelengths go through the same optical channel.

In accordance with specific embodiments, aspects of the presentdisclosure involve 3D super-localization microscopy techniques. Suchtechniques include tracking single biomolecules with fluorescent labelsinside a biological sample, and 3D analysis using other light emittingobjects such as quantum-dots or the scattered light from gold beads ornano-rods. Additionally, various embodiments include use of amicrofluidic device to characterize flow in 3D.

Other specific embodiments include axial-related and/or 3D-relatedmicroscopic localization of multiple point-like light objects labeled indifferent wavelengths as generated using wide-field microscopy. When apoint-like (e.g., sub-wavelength) source of light is positioned at thefocal plane of a microscope, the image that is detected on the imagingcircuitry, such as a camera and/or a detector, is known as the PSF ofthe microscope. A conventional microscope's PSF (e.g., essentially around spot) is used for imaging a two-dimensional (2D) ‘slice’ of aspecimen, and for 2D (x, y) transverse localization of an object withinthat slice. By fitting the shape of the spot with a 2D function such asa centroid, Gaussian, or Airy function, in some instances, the positionof the object can be detected with precision (a process termedsuper-localization). However, objects that are a small distance above orbelow the microscope's focal plane can appear blurry, and furthermore,their depth (or axial distance from the focal plane) is difficult todetermine from their measured image. In accordance with variousembodiments, 3D (x, y, and z) position information is obtained, evenwhen an object is above or below the focal plane. In other embodiments,less than all the 3D information is needed; for example, the axial (z)information alone and/or in combination with some lateral (x or y)information is used instead of the full 3D position information. Using aphase mask, in various embodiments, an additional module is installed ona conventional microscope to solve the blur and depth issues. Instead ofa point of light forming a single ‘spot’ on the camera, light passingthrough the phase mask forms a shape on the camera that looks differentas a function of the object and distance from the focal plane (or amountof defocus).

Various embodiments are directed to an apparatus or method involvingencoding wavelength-based characteristics and 3D positions of aplurality of objects of different wavelengths. In specific embodiments,optics pass light from the plurality of objects toward the image plane.A phase mask is used to modify a shape of the light for each of theplurality of respective wavelengths of light passed from the pluralityof objects. In a number of specific embodiments, the shape of light foreach respective wavelength is different than the shape of the light forother ones of the respective wavelengths. Alternatively, the phase maskmodifies the shape such that the resulting shape (e.g., PSF) is the samefor each respective wavelength. For example, by providing differentphase delays for each wavelength, the phase mask creates a modifiedshape of light for each wavelength that is different and/or the same.Further, circuitry characterizes a 3D image of the plurality of objectsbased on each of the PSFs and the respective wavelengths. In specificembodiments, the circuitry is configured to detect relative movement ofdifferent ones of the objects based on each of the PSFs and therespective wavelengths.

Certain embodiments in accordance with the present disclosure involveoptimizing PSFs with applicable depth ranges far beyond previouslyobtained ranges having a maximum of 2-3 um. As a specific example, usinga phase mask optimized for a particular depth range, super-localizationover a customizable depth range is performed up to 20 um for a 1.4 NAobjective lens (with other parameter-set limitations, such asmagnification, background/signal levels, and noise issues). In specificembodiments, the PSF is used for 3D super-localization and tracking, aswell as for 3D super-resolution imaging in biological samples, sincethis is the applicable depth range used for observing the 3D extent of amammalian cell. However, embodiments are not so limited and the depthrange in various embodiments can be greater than 20 um. The depth range,for example, is a function of system limitations, such as NA objectivelens and the light emitted by the object.

Certain PSFs, in accordance with the present disclosure may be referredto as tetrapod PSFs, due to the shape they trace out in 3D space, as afunction of the emitter position (the position of the object). In anumber of embodiments, the modified shape characterizes the light ashaving two lobes with a lateral distance that changes along a line,having a first orientation, as a function an axial proximity of theobject to the focal plane, and the line having a different orientationdepending on whether the object is above or below a focal plane. Forexample, the different orientation of the line as compared to the firstorientation, in various embodiments, includes a lateral turn of the linefrom the first orientation to the different orientation, such as a 90degree or 60 degree lateral turn. This shape has lines from the centerof a tetrahedron to the vertices, or like a methane molecule. The PSF iscomposed of two lobes, where their lateral distance from one another andorientation are indicative of the z position of the object. Above thefocal plane, the two lobes are oriented along a first line, and belowthe focal plane the two lobes are oriented along a second line that isdifferently orientated than the first line (e.g., perpendicular to thefirst line). For example, the modified shape is created, in variousembodiments, by decreasing the lateral distance (e.g., moving together)of the two lobes along the first line when the object is above the focalplane and is closer to the focal plane (e.g., moving closer), turningthe two lobes laterally, such as 90 degrees, and increasing the lateraldistance (e.g., moving apart) of the two lobes another along the secondline when the object is below the focal plane and is further away fromthe focal plane (e.g., moving away). The tetrapod PSF, as used herein,is not a rotation of a shape of the passing light (e.g., relative to acenter line) as a function of the axial position of the object (as witha spiral and/or helix PSF).

Emitter (e.g., object) localization can be optimally performed usingmaximum likelihood estimation, based on a numerical or experimentallyobtained imaging model. However, other localization methods can be used.While other methods for 3D imaging can be used, such methods usescanning (e.g. confocal), in which temporal resolution is compromised,or parallelizing the imaging system (multi-focal imaging), whichcomplicates the implementation. Certain embodiments in accordance withthe present disclosure do not use a scan or parallelization technique,and include observation of multiple single emitters in a field at highprecision throughout depth ranges, such as discussed above.

In accordance with specific embodiments, aspects of the presentdisclosure involve encoding wavelength (e.g., color) characteristics, inaddition to 3D positions, of a plurality of objects by modifying a shapeof light for each of a plurality of wavelengths of light passed from theobjects and in a single optical path. In specific embodiments, opticspass light from the objects in each of a plurality of wavelengths towardthe image plane and the phase mask. The phase mask is used to modify ashape of light, passed from the object. In various embodiments,modifying the shape of light includes redirecting and modifying thelight to create a PSF for each of the respect wavelengths simultaneouslyusing the same phase mask.

In various embodiments, the phase mask produces different (or same)shapes of light for the different wavelengths by providing a differentphase delay for each of the respective wavelengths. For example, thephase mask modifies the shape of the light by producing a plurality ofPSFs for the respective wavelengths of light. The PSF for eachrespective wavelength is different than the PSF for other ones of therespective wavelengths. For example, the phase mask creates theplurality of PSFs by producing a different phase delay for eachrespective wavelength. In some embodiments, the circuitry generates animage of a plurality of colors, each of the colors corresponding to oneof the wavelengths, on a single optical channel.

The circuitry infers depth information, in addition to thewavelength-based characteristics, about objects that are imaged. Invarious embodiments, the generated 3D image is indicative of respectivedepths of objects that are greater than 3 microns of one another.

For a given application, a desired phase mask (e.g., a pattern) forcertain different wavelengths (or wavelength ranges) can be designed byway of an optimization function that is used for determining an optimalvoltage pattern most applicable to each of the relevant wavelengths. Asan example, a minimization function solves for a pixel-wise weightedleast squares problem to determine the optimal voltage pattern. Theresulting (optimal) voltage pattern (e.g., when placed on an SLM) can beused to create PSFs that are similar to the desired phase masks for eachset of different wavelengths/ranges. These ensuing PSFs (output by thevoltage pattern) are not necessarily identical to a PSF output by thedesired phase masks. The resulting PSFs for each wavelength, however,are similar to the desired phase masks and this relationship can beoptimized for a given set of N wavelengths, for example, using anoptimization function that minimizes a phase distance between thedesired phase mask patterns and the corresponding phase masks.

The phase mask, in some embodiments, is a deformable mirror used to tunethe depth characteristic by deforming. For example, the phase mask tunesa depth characteristic to obtain light from the object at differentrespective depths. In some embodiments, the apparatus and/or method, asdescribed above, includes a tuning circuit used to tune the depthcharacteristic.

In a number of particular embodiments, an apparatus and/or method inaccordance with the present disclosure is used to track objects. Forexample, an apparatus and/or method is used to localize objects thatlabeled in different wavelengths, tracking locations of objects and/orparticles of a plurality of different colors corresponding to thewavelengths simultaneously, and/or characterizing movement of objectswith respect to one another and that are at least 3 microns from oneanother in the axial direction (and any combination thereof).

Certain embodiments involve adjusting phase mask design parameters todeliver optimal performance for a given depth range. Thereby, the phasemask in accordance with the present disclosure is not as limited indepth range as other depth estimation techniques. A module incorporatinga phase mask, in accordance with various embodiments, is installed on anexisting microscope (e.g., commercial microscope) in a short period oftime, such as less than thirty minutes. A phase mask can allow for ahigh numerical aperture (NA) implementation for light-sheet-microscopy.

Turning now to the figures, FIG. 1A illustrates an example apparatus 109in accordance with various embodiments of the present disclosure. Insuch embodiments, the apparatus 109 creates different PSFs for differentwavelengths using a single phase mask 103 and optical channel. The phasemask 103, surprisingly, allows for simultaneous scan-free 3D imaging ofobjects of different wavelengths on a single optical channel. The PSFsallow for precise localization of nanoscale emitters (e.g., objects) in3D over customizable axial (z) ranges of up to 20 μm, with a highnumerical aperture (NA) objective lens. In some specific embodiments,apparatus 109 is used to track movement of multiple objects relative toone another, such as movement of a protein with respect to movement ofother proteins or organelles, simultaneously and in 3D.

An object, as used herein, corresponds to and/or includes an emitter,such as a particle, a molecule, a cell, a quantum dot, a nanoparticle,etc. In various embodiments, a plurality of objects are labeled inand/or emit different wavelengths of light. The plurality of objects arelocated in a sample and imaged using the apparatus 109, as describedherein.

The apparatus 109 includes a phase mask 103 and circuitry 107. The phasemask 103 is arranged with optics 101 in an optical path. For example,the optical path is from the optics 101 to the phase mask 103 to thecircuitry 107. The optics 101 pass light from a plurality of objectstoward the image plane. For example, the optics can include the variouslenses, as illustrated by FIGS. 1B and 2. The phase mask 103 modifies ashape of the light for each of a plurality of respective wavelengths oflight passed from the objects. For example, the objects are of aparticular color corresponding to one of the wavelengths and/or areotherwise labeled in the color. The phase mask 103 includes a patternthat produces a different phase delay for the different wavelengths tocreate the shapes of light for each respective wavelength. For example,the phase mask 103 has an input voltage pattern such that two (or more)wavelengths experience different phase delay patterns resulting in adifferent modification of light (e.g., different PSF and/or sameresulting PSF from different modifications). The phase mask 103 createsthe PSF for each respective wavelength based on a distance of the objectfrom the image plane, as discussed further herein. Unlike other opticalcomponents including, for example, gratings, shape modificationaccordingly to the present disclosure includes a phase-delay pattern(e.g., voltage pattern) for this modification. In accordance with anumber of embodiments, the phase mask has a pattern that includes twopeaks and two valleys, such as a two-dimensional saddle point functionwith two peaks and two valleys.

In some embodiments, the phase mask 103 modifies the shapes of light byredirecting and modifying light passing along the optical path to createthe PSF at or incident upon the image plane for each respectivewavelength. The modification is simultaneous for each respectivewavelength, independent of one another, and from the same optical path.

In a number of specific embodiments, the PSFs created are different foreach wavelength. For example, the phase mask 103 modifies the shape oflight for each respective wavelength differently than the shape of lightfor other ones of the respective wavelengths and resulting in differentshapes of light for each wavelength. The different shapes for eachrespective wavelength are created by the phase mask 103 providingdifferent phase delays for the each of the respective wavelengths.Thereby, the phase mask 103 modifies the shapes of lights to create aplurality of PSFs for the wavelengths of light, the PSF for eachwavelength being different than the PSF for other ones of the respectivewavelengths. In other specific embodiments, the PSFs created are thesame for each wavelength of light. For example, the phase mask 103modifies the shape of light differently for each respective wavelength,resulting in a PSF for each wavelength that is the same. Modifying theshapes as the same shape, in a number of embodiments, is used forchromatic aberration correction.

The phase mask 103, in various embodiments, is placed in the Fourierplane to modify light in the optical path. For example, the phase mask103 modifies the shape of light by redirecting and modifying the lightpassing along the optical path to create a PSF for each wavelength atthe image plane (e.g., the circuitry 107). The shape modificationincludes a shape of light as a function of an axial proximity of theobject, such as a tetrapod PSF. In a number of embodiments, the shape oflight is characterized by having two lobes with a lateral distance thatchanges along a line, having a first orientation, as a function an axialproximity of the object to the focal plane, and the line having adifferent orientation depending on whether the object is above or belowa focal plane. In some specific embodiments, the lateral distancedecreases as a function of the axial proximity of the object to thefocal plane. For example, as the object gets closer to the focal plane,the lateral distance decreases. Similarly, as the object gets fartheraway from the focal plane, the lateral distance increases.

The phase mask 103 creates such PSFs, in various embodiments, bydecreasing the lateral distance (e.g., moving together) of the two lobesalong the first line when the object is above the focal plane and iscloser to the focal plane (e.g., moving closer), turning the two lobeslaterally, such as 90 degrees, and increasing the lateral distance(e.g., moving apart) of the two lobes another along the second line whenthe object is below the focal plane and is further away from the focalplane (e.g., moving away). The second line is at an angle, based on thelateral turn of the two lobes, to the first line.

The phase mask 103 creates any of a variety of axially-dependent PSFs,where different wavelengths produce different PSFs so that they may bedistinguished.

The apparatus 109 further includes circuitry 107 to characterize a 3Dimage of the objects based on the light detected via the circuitry 107which includes computational image processing. The circuitry 107 usesthe modified shapes of light and the respective wavelengths to provide3D characteristics (x, y, and z based characteristics) of the objects.The 3D characteristics include the 3D position information and/or anaxial dimension (z). For example, the circuitry 107 infers depth of eachobject of the different wavelengths based upon the PSFs. In variousembodiments, the circuitry 107 includes an imaging circuit. The imagingcircuit is in the image plane (e.g., the final image plane) and detectslight at or incident upon the imaging circuit.

In various embodiments, the circuitry 107 generates the 3D image that isindicative of respect depths of portions of the object that are at least3 um from one another. For example, the circuitry 107 infers depth ofportions of the object based upon a 3D shape of the objects on the imageplane and a location of the objects from the modified shape of lights.In various embodiments, the circuitry 107 infers the depth of portionsof the object based computational analysis of the image shapes, asdiscussed further herein.

In a number of embodiments, the circuitry 107 encodes wavelength-basedcharacteristics, in addition to 3D positions, of the objects based onthe PSFs created by the phase mask 103. Encoding the wavelength-basedcharacteristics allows for the circuitry 107 to localize the objectslabeled in different colors, such as particles, in 3D based on the PSFs.Wavelength-based characteristics, as used herein, is informationindicative of an object's emitted wavelength(s) useful fordistinguishing the object by its corresponding wavelength(s) for a givenapplication. For example, in various embodiments, wavelength-basedcharacteristics include the wavelength, frequency, emission spectrum,spectrum of the color, resulting phase delay and/or PSF corresponding tothe wavelength, among other characteristics indicative of wavelength. Invarious embodiments, the expected PSFs for each wavelength as created bythe phase mask 103 are calculated and the expected shapes of the PSFsare provided as a library (e.g., stored using the circuitry 107). Insome embodiments, the expected PSFs for each wavelength include(tetrapod-type) PSFs for various axial z-ranges of the objects.

The circuitry 107 characterizes a 3D image of the objects from lightdetected. For example, the circuitry 107 concurrently localizes theplurality objects in the single optical path based on the modifiedshapes of lights for each respective wavelength. The localizationincludes three-dimension locations (e.g., x, y, and z). Concurrentlocalization, in some embodiments, includes tracking locations of theobjects of a plurality of colors, each color corresponding to one of thewavelengths. As a specific example, locations of the objects in 3D aretracked by the circuitry 107 (and using a single optical channel) over aperiod of time and simultaneously based on the encoded wavelength-basedcharacteristics and the modified shapes of light. As another specificexample, the circuity 107 concurrently tracks 3D locations of twoparticles that are labeled using different colors using the encodedwavelength-based characteristics.

In various embodiments, the phase mask 103 tunes the depthcharacteristics to obtain light from the object at different respectivedepths. For example, the apparatus 109 includes a tuning circuit thatmanipulates the phase mask 103 to tune the depth characteristics. Insuch embodiments, the phase mask 103 includes a deformable mirrorconfigured to tune the depth characteristics. A deformable mirrorincludes a mirror face-sheet that is attached to an array of post and anactuator array. For example, each post is centered an actuator array.The actuator array includes a flexible cantilever that is suspended overan actuator electrode. Further, the entire mirror face-sheet andactuator array is fabricated on a silicon wafer, in various embodiments.For more specific and general information regarding a deformable mirror,reference is made to Appendix C of the underlying provisional entitled“Appendix C”, which is fully incorporated herein by reference.

A number of embodiments include a family of (tetrapod-type) PSFs. Thespecific phase mask design (corresponding to a certain PSF from thetetrapod family) is dependent on the apparatus parameters, mainly on thedepth range. For different imaging apparatus parameters (magnification,numerical apertures, etc.), the phase mask 103 is optimized using anoptimization routine, as discussed further herein. For example, thephase mask 103 yields slightly different phase mask patterns for arespective wavelength depending on the axial position of the objectassociated with the wavelength. Related embodiments in accordance withthe present disclosure utilize PSF engineering to provide optimized,high-precision localization capability, for a large depth range. Forexample, such a phase mask design can yield a depth range of 2-20 um fora 1.4 NA objective lens (with other parameter-set limitations, such asmagnification, background/signal levels, and noise issues). In someembodiments, the tetrapod PSF is tailored and optimized to a specificdepth range, which is dependent on and/or defined as a function of theinformation encoded in the PSF, as well as the NA objective lens and thelight emitted by the object. Surprisingly, it has been discovered, withsuch a tetrapod-type PSF, the information for a given amount of lightemitted by an object and for a given NA objective lens has asignificantly greater precision than other PSFs, although other PSFdesigns (not illustrated by the specific examples disclosed herein) canbe used for implementing this invention

In some embodiments, a number of functions (e.g., equations andalgorithms) for specifying the exact design of a phase mask 103 (e.g.,parameterized phase mask) are used based on the system parameters of agiven imaging application. In addition, in various embodiments, thelocalization of an emitter given a measured image of the PSF isperformed using maximum-likelihood-estimation. In a number ofembodiments, a module (e.g., computer-readable code) is executed by thecircuitry 107 of the apparatus 109 to perform both of these actions,including the imaging model (as discussed further herein). At the sametime, a set of phase masks is calculated to produce tetrapod PSFs forvarious fixed z-ranges, and the expected shapes of the PSFs are providedas a library (e.g., stored using the circuitry 107). In accordance withvarious embodiments, no calculation is required by the user except toperform fitting of the acquired images using interpolation of imagesfrom the library. Although embodiments are not limited to tetrapod PSFsand in various embodiments the library include expected PSFs for otherexample PSFs.

FIG. 1B illustrates an example apparatus in accordance with variousembodiments. As illustrated, the apparatus includes a modifiedmicroscope. The apparatus includes a phase mask 106 that is installed inan optical path (e.g., detection pathway) of the microscope. Phasemasks, in accordance with various embodiments, allow for precise 3Dlocalization of multiple objects (e.g., emitters) labeled in differentwavelengths over a customizable depth range. The customizable depthrange, in some embodiments, is up to 20 um for a 1.4 numerical aperture(NA) objective lens. The phase mask 106, in various embodiments, is usedto simultaneously track the location of the multiple objects, in thedifferent wavelengths, at different depths, allowing scan-free highspeed imaging.

As illustrated, the apparatus includes an optical path that includesoptics 104, 108 configured to pass light from objects 112-1, 112-2 froman object plane 102 toward an image plane 110. The objects 112-1, 112-2are labeled in different colors corresponding to different wavelengthsof lights. In various embodiments, the wavelengths are separated by atleast 60 nanometers (nm) from one another (e.g., 540 nm and 600 nm),although embodiments are not so limited. A phase mask 106 is arrangedwith the optics 104, 108 to modify the shape of light passed from theobjects 112-1, 112-2. For example, in some embodiments, the phase mask106 is positioned between the objective lens 104 and a tube lens 108.

Such circuitry can be located at the image plane 110 for generating a 3Dimage from light detected at the image plane 110 using the modifiedshape to provide depth-based characteristics of the object 112. Thecircuitry, in various embodiments, includes imaging circuitry. Theimaging circuitry is circuitry commonly used with digital signal imageprocessing (such image circuitry includes, e.g., a charge-coupled device(CCD), image sensors based on field-effect technology such as CMOS imagesensors, and the like).

FIG. 2 illustrates an example apparatus in accordance with variousembodiments. As illustrated, the apparatus includes a modifiedmicroscope. The apparatus of this example apparatus is a standard(inverted) microscope, augmented by a 4 f optical processing system. ThePSF of the microscope is modified from that of a standard microscope bycontrolling the phase of the electromagnetic field in the Fourier planeof the 4 f system using a phase mask 228. In various embodiments, thePSF is modified for each wavelength of light using the phase mask 228,which is placed in the Fourier plane of the microscope. The phase mask228, in various embodiments, includes a (dielectric) phase mask or aliquid crystal-based spatial light modulator (SLM).

As indicated above, the placement of the phase mask in the Fourier planecan be advantageous. At this location, the phase function produced bythe phase mask multiplies the Fourier transform of the image. This meansthat the operation of adding the mask works throughout the field ofview. In this context, all single-emitter spots get the new PSF (this isreferred to as shift invariance). If the mask is placed elsewhere,something else will happen and the PSF would vary across the field ofview. The Fourier plane is also sometimes referred to as the “back focalplane” and “pupil plane” because both of these are conjugate to theFourier plane.

As illustrated by FIG. 2, the apparatus includes an optical path. Theoptical path is from the objects in the sample 214 to the image plane223. The optical path illustrated in the example of FIG. 2 includes thefollowing optics/planes configured to pass light from the objects towardthe final image plane 223: objective lens 216, dichroic element 218,tube lens 220, intermediate image plane 222, lens 224, polarizer 226,phase mask 228, and lens 230. The optics include one or more focusinglenses (e.g., the objective lens 216) and a light source to illuminatean object 214. Various other focusing lenses (including the otherillustrated lenses of FIG. 2 can be used to focus the light, afterinteracting with the objects, to the final image plane for detection bycircuitry. The phase mask 228 can be located between the intermediateimage plane 222 and the final image plane 232, in various embodiments.For example, the phase mask 221 is placed in the back focal plane of theillustrated optics and input focal plane of other optics. Onceimplemented, an apparatus, consistent with that shown in FIG. 2, can beused to accomplish 3D imaging of objects, and encode wavelength-basedcharacteristics including the axial position of the objects.

The phase mask 228, in some embodiments, is placed in between the twooptics 224/230. The phase mask in various embodiments is a dielectricphase mask, a SLM, a hologram, a computer-generated hologram, adiffractive optical element, a volume optical element, or the like. Thephase mask may have one or both of amplitude and phase components. Themask 228 may be static or dynamic, based upon the scene being imaged,system requirements, or user requirements. The mask 228 may beimplemented with a spatial light modulator which manipulates the phaseand/or the amplitude of the light. Examples of such masks include thoseconstructed from liquid crystals or from micro-electro-mechanicalsystems. Further, a physical mask can also be fabricated, for example,by electron beam lithography, proportional reactive ion etching in SiO₂,hot embossing in PMMA, gray level lithography, multistepphotolithography, or direct laser writing.

The light source in a number of embodiments includes a coherent lightsource. The coherent light source may include, for example, an Argon ionlaser operating at 488 or 514 nm, or a diode laser emitting at 532 nm or641 nm. Other lasers operating at various wavelengths may also be usedas sources of coherent light. The light source may produce monochromaticor polychromatic light. The optics expand or reduce the laser beam sothat it illuminates a region of interest of the objects. These opticsmay also be supplemented by polarizers 226, waveplates, or diffusers inorder to manipulate the polarization or coherency of the lightilluminating the object. Other light sources that produce incoherentlight, such as an arc lamp, may also be used. The focus elements maycomprise, for example, coated achromatic lenses with 150 millimeter (mm)focal length and an aperture of 50 mm. However, these focus elements maybe of different focal lengths in order to accomplish beam expansion orreduction. Various other lenses or optical components may also beincluded in order to focus light from the object onto the detector.

The circuitry, in various embodiments, encodes a wavelength-basedcharacteristic of a plurality of objects by modifying a PSF for eachwavelength at the circuitry using a phase mask. The circuitryadditionally encodes axial position of each of the objects using one ormore parameterized phase masks. For example, the one or moreparameterized phase masks are optimized for a target depth-of-fieldrange for an imaging scenario. The apparatus, for example, provides atarget depth-of-field of greater than 2 um and up to at least 20 um fora 1.4 NA objective lens. The depth range of the PSF is dependent on anddefined as a function of the information encoded in the PSF, as well asthe NA objective lens and the light emitted by the object. Surprisingly,it has been discovered that with a (tetrapod-type) PSF, the informationfor a given amount of light emitted by an object and for a given NAobjective lens has a greater precision than other PSFs. Encoding anaxial position in various embodiments includes localizing multipleparticle in 3D based on the modified PSFs for each wavelengthcorresponding to a respective particle (e.g., a tetrapod PSF), and/ortracking locations of the multiple particles simultaneously based on theencoded axial position.

FIGS. 3A-3B illustrate an example of fluorescent beads imaged using anapparatus, in accordance with various embodiments. In accordance withvarious embodiments, using the above described imaging apparatus withPSF engineering (e.g., the 4 f optical system with phase mask in theFourier plane), a pattern is designed that simultaneously produces a PSFfor each of a plurality of different wavelengths of light. Suchembodiments allow for simultaneous scan-free 3D imaging of objects withdifferent wavelengths using a signal optical channel (e.g., a singlecamera/detector).

Such embodiments are implemented by using a phase mask, such as adielectric phase mask and/or a liquid crystal SLM. The phase mask has athickness such that at any point on the phase mask produces a differentphase delay for different wavelengths. This is performed by takingadvantage of the refractive index change between the material the phasemask is formed of (e.g., quartz) and air. In some embodiments, the phasemask includes an SLM. In such embodiments, different phase delays arefrom the spectral dispersion properties of the SLM.

For example, FIGS. 3A-3B illustrates measurements of fluorescent beads(e.g., tetraspeck spheres), taken with different light sources (e.g.,excitation laser) and emission filters, but using the same designedpattern on the phase mask (e.g., an SLM). The fluorescent beads are infocus (e.g., z=0) such that the reason they appear to have differentshapes (vertical spots v. horizontal spots) is because they are emittingat different wavelengths. FIG. 3A illustrates an image 334 generatedusing a phase mask of fluorescent beads that are labeled in a wavelengthof 670 nm. FIG. 3B illustrates an image 336 generated using the phasemask of the same fluorescent beads but that are labeled in a wavelengthof 530 nm. That is, the images 334, 336 are of the same beads that areimages using the same phase mask that appear different due to beinglabeled at different wavelengths and thus emitting light at thedifferent wavelengths.

In some embodiments, the phase mask includes a liquid-crystal SLM. Aliquid-crystal SLM translates an input voltage pattern into aphase-delay pattern. For example, as discussed below, FIG. 4 illustratesa voltage pattern used to produce data illustrated by FIGS. 3A-3B.

FIG. 4 illustrates an example of a SLM voltage pattern 438 in accordancewith various embodiments. The voltage pattern 438 applied to the SLMcreates two phase patterns, one for each wavelength, to produce theimages of FIGS. 3A-3B. The gray level represents the possible range of256 input voltages on a SLM, although embodiments in accordance with thepresent disclosure are not limited to 256 input voltages and can includeinput voltages that are greater or less than 256.

Multi-wavelength phase masks, in various embodiments, include morewavelengths and objects than illustrated by FIGS. 3A-4. For example,various embodiments include two to ten objects that are labeled usingdifferent colors, each of the different colors corresponding to adifferent wavelength, resulting in two to ten desired PSF responses. Forexample, FIGS. 5A-5B illustrate a 32 gray level dielectric phase mask,designed to produce four different PSFs for four different wavelengths.

FIGS. 5A-5B illustrate an example phase mask and PSF for differentwavelengths created using the phase mask, in accordance with variousembodiments. FIG. 5A illustrates the PSFs 540, 542, 544, 546 generatedfor four different wavelength ranges (e.g., 655 nm, 605 nm, 550 nm, and550 nm, respectively) by the phase mask 548, all at z=0. FIG. 5Billustrates the phase mask 548 (e.g., a 32 gray level dielectric phasemask pattern) designed to create the four different PSFs 540, 542, 544,546 for four different wavelengths.

In various embodiments, the phase mask 548 is capable of providing 3Dimages (x, y, and z information) using the PSFs 540, 542, 544, 546. Thatis, each PSF for a particular wavelength changes its shape as a functionof the z position of the object, similar to a single-color phase maskthat creates a tetrapod PSF. The applicable z-range of amulti-wavelength phase mask may be smaller than that of a single-colorphase mask, in some embodiments, in order to avoid ambiguities betweendifferent wavelengths at different z values. For example, in someembodiments, the z-range of the multi-wavelength phase mask is splitbetween the different wavelengths.

Alternatively, in some embodiments, the multi-wavelength phase mask isnot a tetrapod phase mask (e.g., is not similar to the single-wavelengthphase mask, as described in further detail by the underlying ProvisionalApplication (Ser. No. 62/146,024) and the corresponding Non-ProvisionalApplication entitled “Apparatuses and Methods for Three-dimensionalImaging of an Object” filed on the same day as the present applicationand claiming benefit to the same underlying Provisional Application).For example, the PSF for the different wavelengths can be general, asillustrated by FIG. 6.

FIG. 6 illustrates an example phase mask, in accordance with variousembodiments. The phase mask 660 (e.g., pattern) illustrated by FIG. 6includes a dual-wavelength phase mask. A dual-wavelength phase mask, asused herein, includes a phase mask configured to create modified shapesof light (e.g., PSFs) simultaneously for two different wavelengths oflight using a single optical channel. As illustrated, the modifiedshapes of light 662, 664 resulting from the phase mask 660 for an objectemitting red (e.g., wavelength of 670 nm) appears as the word red and anobject emitting green (e.g., wavelength of 560 nm) appears as the wordgreen. The gray levels 661 represent etching depth in quartz, in unitsof microns. The phase mask 660 results in two PSFs at z=0 thatcorrespond to the two different wavelengths (e.g., red and green).

FIGS. 7A-7D illustrate an example of a dual-wavelength phase mask, inaccordance with various embodiments. For example, FIG. 7A includes agraph that illustrates a phase delay versus voltage for two differentwavelengths of 559 nm depicted as 766 (e.g., green) and 669 nm depictedas 767 (e.g., red). The differences of the phase delay versus voltagebetween the two wavelengths arise, for example, from the spectraldependency of the phase mask. Based on these relations, an input voltagepattern is applied to the SLM phase mask as illustrated by FIG. 7B. FIG.7B illustrates the voltage pattern mask 768 which will produce differentphase responses illustrated by FIG. 7A. The voltage pattern 768 isillustrated in an 8-bit gray scale 769, although embodiments are not solimited. The voltage pattern 768 applied to the SLM modifies shapes oflights for the two different wavelengths by different phase delays andresults in two different PSFs.

FIG. 7C illustrates an image of two in-focus (z=0) fluorescent objects(e.g., microspheres) with peak emission wavelengths of 559 nm and 699 nmwhen the voltage pattern 768 is not used and/or is turned off. FIG. 7Dillustrates the same two florescent objects imaged using the SLM voltagepattern shown in FIG. 7B. As illustrated, by using the voltage pattern768, the resulting PSFs are wavelength dependent, where the PSFs fromthe two objects spell out the words “red” and “green” respectively(corresponding to the plots depicted at 766 and 767 of FIG. 7A). Thescale bar of FIGS. 7C-7D includes 5 um.

The resulting PSFs, for multi-wavelength applications, are not limitedto that illustrated by FIG. 7D. For example, PSFs that encode the axialposition are beneficial for a variety of applications. There are variousways to distinguish between wavelengths, since the phase delayexperienced by the different wavelengths is directed differently, invarious embodiments, thus giving design freedom. For example, variousembodiments include optimizing the phase mask for multi-wavelength formultiple object tracking and/or super-resolution imaging. Eachapplication uses different PSF designs.

For certain applications the above-disclosed approaches are used forcharacterizing different wavelength-distinguishable objects. As anexample, such applications are realized through methods and systems thatare applied and useful where the distinguishable objects are closelyrelated at a molecular level as indicated by their light emissions.Thus, where a phase mask has been optimized for one of the objects, theresulting PSF would be slightly-less than optimized for theclosely-related molecular object. By recording and tabulating thecorrelations between the (varied) PSFs and different closely-relatedmolecular objects, identification and differentiation is realized forentire classes of such closely-related objects. Among other uses of suchinformation is the ability to define by optimization as disclosed hereinphase mask specific to these closely-related objects.

More Specific/Experimental Embodiments

FIGS. 8A-8G illustrate a dual-wavelength phase mask and correspondingPSFs for two different wavelengths, in accordance with variousembodiments. The voltage pattern 876, as illustrated by FIG. 8C, isdesigned for multi-wavelength 3D localization over a depth range ofbetween 2-20 um (and beyond). The resulting SLM voltage patter 876creates a tetrapod PSF. In accordance with a number of embodiments, a(tetrapod-type) PSF is a characterization of light having two lobes witha lateral distance that changes along a line, having a firstorientation, as a function of an axial proximity of the object to thefocal plane, and the line having a different orientation depending onwhether the object is above or below a focal plane. In relatedembodiments, the tetrapod PSF is composed of two lobes, where theirdistance and orientation are indicative of the z position of theemitter. Above the focal plane, the two lobes are oriented along a firstline, and below the focal plane the two lobes are oriented along asecond line that is at an angle (e.g., perpendicular) to the first line.For example, the modified shape is created, in various embodiments, bydecreasing the lateral distance (e.g., moving together) of the two lobesalong the first line when the object is above the focal plane and iscloser to the focal plane (e.g., moving closer), turning the two lobeslaterally, such as 90 degrees, and increasing the lateral distance(e.g., moving apart) of the two lobes another along the second line whenthe object is below the focal plane and is further away from the focalplane (e.g., moving away).

As described above, a feature of the tetrapod PSF is two lobes that varyin separation as function of the object depth. The axis along which thelobes separate rotates a particular lateral degree, such as 90 degrees,depending on whether the object is above or below the focal plane. Theapplicable z-range of a tetrapod PSF is 2-20 um for a 1.4 NA objectivelens. To distinguish between two wavelengths, the second PSF, in variousembodiments, is rotated by 45 degrees as illustrated by FIGS. 8A-8G.

FIG. 8A illustrates a desired phase mask 872 (e.g., a pattern) for a 669nm wavelength (red) and FIG. 8B illustrates a desired phase mask 874 fora 559 wavelength (green). The desired phase masks 872, 874 are input toan optimization function to solve for a pixel-wise weighted leastsquares problem to determine the optimal voltage pattern. FIG. 8Cillustrates the resulting voltage pattern 876 (e.g., the optimal voltagepattern). The resulting voltage pattern 876 when placed on the SLMcreates PSFs that are similar to the desired phase masks for eachwavelength. The PSFs output by the voltage pattern 876 are not identicalto PSF output by the desired phase masks 872, 874 as a compromise isfound using the optimization function for both wavelengths. However, asillustrated by FIGS. 8D-8G, the resulting PSFs for each wavelength880,882 are similar to the desired phase masks 872, 874.

An example optimization function includes for a given set of Nwavelengths λ_(i), i=1 . . . N and N corresponding desired phase maskpatterns D(x, y)_(i), i=1 . . . N, a voltage pattern V (x, y) is soughtthat minimizes a weighted least squared phase distance between all Ndesired phase mask patterns and the corresponding phase masks. Thefollowing pixel-wise optimization is performed:

${v_{xy} = {\arg\;\min{\sum\limits_{i = 1}^{N}{w_{i} \cdot {{Dist}_{2\;\pi}\left( {{P_{i}\left( v_{xy} \right)},D_{{xy},i}} \right)}^{2}}}}},$Where P_(i)(v) is the phase delay that wavelength λ_(i), experienceswhen voltage v is set on the phase mask pixel, and the phase distancefunction is defined as:

${Dist}_{2\pi}\left( {a \cdot {b\left( {= {2{\pi \cdot {{{\frac{a - b}{2\pi} - \left\lbrack \frac{a - b}{2\pi} \right\rbrack}}.}}}} \right.}} \right.$Further, since the addition of a contact phase to a desired phasepattern is allowed, the degree of freedom is optimized.

FIG. 8D illustrates a calculated phase delay 880 (e.g., a PSF)experienced by a wavelength of 699 nm using the phase mask 876. FIG. 8Fillustrates PSFs created for a 40 nm red microsphere in a 20 um z-rangeat the top and theoretically desired at the bottom. For example, thePSFs 883-1, 883-2, 883-3, 883-4, and 883-5 are created using the SLMvoltage pattern 876 in response to the red microsphere having az-position of −10 um, −3 um, 0 (e.g., in focus plane), 3 um, and 10 umrespectively.

FIG. 8E illustrates a calculated phase delay 882 (e.g., a PSF)experienced by a wavelength of 559 nm using the voltage pattern 876.FIG. 8G illustrates PSFs created for a 40 nm green microsphere in a 20um z-range at the top and theoretically desired at the bottom. Forexample, the PSFs 885-1, 885-2, 885-3, 885-4, and 885-5 are createdusing the SLM voltage pattern 876 in response to the red microspherehaving a z-position of −10 um, −3 um, 0 (e.g., in focus plane), 3 um,and 10 um respectively.

In various embodiments, a phase mask pattern is designed tosimultaneously track different colored objects in 3D as the objectsrandomly diffuse in solution, such as water with around 55 percentsucrose. FIGS. 9A-D illustrate such a design.

FIGS. 9A-9D illustrate an example of 3D localization of two differentlylabeled objects using a multi-wavelength phase mask, in accordance withvarious embodiments. For example, FIG. 9A illustrates an example 50millisecond movie frame with a red microsphere 987 and a greenmicrosphere 988. The phase mask is used to generate the image, invarious embodiments, by creating a tetrapod PSF with a 45 degreerotation between the two colors as previously illustrated by FIGS.8A-8G. As the microspheres 987, 988 diffuse freely, they are tracked fora period of time, such as 45 seconds. In each frame, the microspheres987, 988 are localized using a maximum likelihood estimation (MLE)fitting to a numerical PSF model. In some embodiments, two trajectories,one for each microsphere, are obtained. FIG. 9B illustrates themean-squared displacement curves (MSD) for the microspheres 987, 988.For example, the red microsphere 987 corresponds to the MSD 989 and thegreen microsphere 988 correspond to the MSD 990. FIG. 9C illustrates a3D trajectory of the red microsphere 987 and FIG. 9D illustrates a 3Dtrajectory of the green microsphere 988. The axes units are in um (e.g.,scale bar in 5 microns) and the grey scale encodes time in seconds.

From the MSD curves 989, 990, the diffusion coefficient of eachmicrosphere 987, 988 is obtained in a number of embodiments. The ratiobetween the measured coefficients (D_(red)=0.52±0.045 um²/s,D_(green)=0.27±0.023 um²/s) corresponds to theory, as D scales like theinverse of the radius in the Einstein-Smoluchowski relation:experimental D_(green)/D_(red)=0.52±0.09 um²/s and theoreticalD_(green)/D_(red)=0.48±0.009 um²/s. The average localization precisionper frame, obtained by localizing immobilized microspheres under similarimaging conditions is (20, 24, 45) nm for the green microsphere 988 (foran 18,000 average detected signal photons per frame) and (12, 13, 39) nmfor the red microsphere 987 (for an average of 34,000 detected signalsphotons per frame).

In various specific embodiments, diffusion is carried out in a 55% (w/v)sucrose aqueous solution. For example, two cover glass slides areadhered with doubled sided tape to form a diffusion chamber ofapproximately 50 um in height. A dilute concentration of fluorescentmicrospheres is added to the solution and allowed to diffuse at roomtemperature.

The freedom in designing multi-wavelength phase masks enables manyapplications. For example, specific embodiments involve tracking 3Dparticles that are differently labeled, such asdifferently-color-labeled biomolecules that are interacting and known tobe in proximity. In such a case, the different PSFs overlap in imagespace, making fitting challenging. To overcome this challenge, variousembodiments include adding a linear phase ramp to one of the phasemasks. The linear phase ramp results in a lateral shift of the PSF ofone of the wavelengths.

In accordance with some embodiments, object locations of tetrapod PSFdata is performed using a maximum likelihood estimation with a numericalscalar imaging model, taking into account refraction index mismatch andusing Matlab code.

FIGS. 10A-10C illustrate an example of multi-wavelength super resolutionimaging using a multi-wavelength phase mask, in accordance with variousembodiments. In various embodiments, a multi-wavelength phase mask isused for simultaneous multi-wavelength super-resolution imaging, such asof biological specimen. For example, a fixed BS-C-1 cell is imaged, withmicrotubules marked by anti-alpha-tubulin primary antibodies labeledwith a red fluorescent die, such as Alexa646, and mitochondria markedvia anti-ATPB primary and a green fluorescent die, such asAlexa532-labeled secondary antibodies.

Multi-wavelength imaging is performed by acquiring a plurality of imagesof blinking single molecules. For example, a sequence of images isacquired. In contrast to conventional microscopes, various embodimentsinclude exciting both color labels simultaneously, and recorded on thesame region of the apparatus (camera). Further, the wavelength (e.g.,color) characteristic of each object is encoded in the resulting PSFshape.

A parameter that determines the precision to which one can localize anobject is the number of detected photons. The-phase only liquid crystalSLM, for example, is designed to modulate one polarization of light. Thelight polarization in the unmodulated direction is filtered out, invarious embodiments, by a polarizer upstream from the SLM. To takeadvantage of the maximal number of signal photons, in a number ofembodiments, both polarizations of light are used that are impinging onthe SLM. The light polarization that is not modulated by the liquidcrystal SLM produces a standard PSF in the image plane. To encodewavelength characteristics, the other polarization is modulated by themulti-wavelength mask by laterally shifting the standard PSF in they-direction for a first wavelength using a phase ramp, such ascorresponding to red, and in the x-direction for a second wavelengthusing a phase ramp, such as corresponding to green. The combined resultof both polarizations in the image plane is a PSF that is elongatedvertically for the first wavelength and horizontally for the secondwavelength (e.g., see FIG. 10A).

Example super-resolution imaging is illustrated by FIGS. 10A-10C. Forexample, FIG. 10A illustrates raw data recorded from a super-resolutionimaging movie. Two example PSFs of a first wavelength 1092 (e.g.,vertically elongated) and a second wavelength 1091 (e.g., horizontallyelongated) are enlarged in the inset with the arrows showing theelongation direction. In various embodiments, approximately 430,000emitters are localized in a 61,000 frame movie. Each identified objectis localized using the identified PSFs and a 2D Gaussian fit, and colordiscrimination is performed according to the direction of elongation(for example, horizontal is green and vertical is red). The attainableresolution is demonstrated by the microtubule FWHM of 53 nm obtainedfrom a histograms of locations in the microtubule section. FIG. 10Billustrates a super-resolution image obtained by localizing each objectin the moving and assigning its wavelength (red is microtubules andgreen is mitochondria). The inset illustrates the diffraction limiteddata. FIG. 10C illustrates a histogram of localizations within thedotted white box surround a microtubule section of around 2 um in FIG.10B, and the diffraction limited intensity cross-section from the sameregion. Considering a known microtubule diameter of around 25 nm, thiscorresponds to a localization precision (e.g., a standard deviation) ofaround 21 nm, which is corroborated by repeatedly localizing singlemolecules that are on for multiple frames in the movie and calculatingthe standard deviation in localization.

In a number of specific embodiments, for cell imaging, cultured BS-C-1(Ceropithecus aethiops epithelia kidney, ATCC CCL-26) cells are plantedonto glass coverslips and cultured for 48 hours in high glucose, DMEMmedia containing 10% (v/v) fetal bovine serum. Cells are fixed inchilled 4 percent (w/v) paraformaldehyde for 20 minutes and incubatedwith 10 milliMole(mM) NH₄CL for ten minutes. Cells are permeabilizedwith three times washing steps containing 0.2% (v/v) Triton-X 100 in pH7.4 PBS with a five minute incubation between each wash and placed inblocking solution (3 percent w/v BSA in PBS) for one hour beforelabeling for two hours with Alexa-647-labeled monoclonal rabbitanti-alpha-tubulin primary antibodies (ab190573) and mousemitochondrial-marking anti-ATPB primary antibodies (an14730) using 1:200dilution in 3% w/v BSA. Cells are washed three times with 0.2% Triton-X100 with three minutes waiting between each wash. Goat anti-mouse Alexa532-conjugated secondary antibody (A11002) labeling is then performedwith 1:500 dilution for one hour followed by five washing steps of 0.2%Triton-X 100. Samples are shielded from light and kept at four degreesCelsius until imaged.

Super-resolution imaging is performed 2-3 days after fixing cells.Samples are placed in a cover glass holder, warmed to room temperature,and placed in a blinking media (700 ug Glucose Oxidase, 50 ug/mLcatalase, 0.55M Glucose, 140 mM 2-Mercaptoethanol, all Sigma in 0.1M pHTris.HCl buffer). The sample is scanned at low-intensity laserillumination for suitable regions and imaged with 10 kW/cm² intensity641 nm light and 5 kW/cm² intensity 514 nm light, with a risingintensity of the 405 nm activation laser (0-500 W/cm²).

FIG. 11 illustrates an example 3D rendering of tetrapod PSF, inaccordance with various embodiments. For instance, the 3D rendering ofthe tetrapod PSF 1113 includes a 6 μm tetrapod PSF image plane intensityas a function of the emitter's axial position away from the focal plane(at z=0). The intensities making up the 3D shape are threshold forvisibility. Three slices of the PSF are shown with no thresholding (atz=−3,0,3 μm), displaying the full dynamic range of intensity. Scale baris 1 μm. As illustrated, in some embodiments, the PSF is created by 2lobes 1105-1, 1105-2 moved along a first line 1111 above the focalplane, turned 90 degrees, and moved along a second line 1125 below thefocal plane. The second line 1125 is perpendicular to the first line1111. Accordingly, in some embodiments, the modified tetrahedral shapeis a characterization of light having two lobes with a lateral distancethat changes along a line, having a first orientation, as a function ofan axial proximity of the object to the focal plane, and the line havinga different orientation depending on whether the object is above orbelow a focal plane (e.g., two lines from the center to two lobes1105-1, 1105-2 orientated along a first line 1111 when the object isabove the focal plane and two lines from the center to the two lobesoriented along a second line 1125 when the object is below the focalplane, the second line 1125 being perpendicular to the first line 1111).

FIGS. 12A-12B illustrate examples of a light sheet microscope, inaccordance with various embodiments. In various embodiments, theapparatus includes a light sheet microscope (LSM) as illustrated by FIG.12A. The LSM, at any given time, illuminates a slice of a sample and/oran object, around 2 um thick, by a sheet of light. LSM, in variousembodiments, utilizes a tilted illumination 1295 relative to the focalplane. For example, optics 1293 and a scanning mirror 1294 areconfigured and arranged to provide the illumination 1295, a slice of thesample 1296 and/or the object at a time. Thereby, the optics pass asheet of light through the sample 1296 and/or the object and the lightfrom the object propagates toward the imaging plane. The scanning mirror1294, in various embodiments, is utilized to adjust the height of thelight sheet in the sample. Light emitted 1299 from the slice of thesample is detected using circuitry 1298, such as imaging circuitry. FIG.12B illustrates an example of illuminating 1295 a slice 1297 of a sample1296 at a time using an LSM, such that only portions of the sample 1296are illuminated at a given time.

In various embodiments of the present disclosure, an LSM (e.g., arelatively simple LSM) is used because the depth information is alreadyencoded in the PSF shapes and the sample 1297 is illuminated in adescending angle relative to the field of view. For example, the z-sliceilluminated by the LSM is not parallel to the focal plane of theobjective, but rather, it is tilted by some angle. Due to the largedepth range, PSFs in accordance with certain embodiments of the presentdisclosure provide an angle that is steep (tens of degrees). Therefore,imaging is performed all the way down to the substrate, and the lightsheet is scanned in the axial direction to cover the entire sample.

Various embodiments include an imaging modality based on optimizedtetrapod PSFs, capable of high-precision imaging throughout a tunableaxial range. For example, large-axial-range tracking in a microfluidicdevice is performed, tracking under biological conditions of a Quantumdot-labeled molecule diffusing on the membrane surface of live mammaliancells, as well as single-fluorophore localization capabilities over a 7μm axial range. Thereby, the tetrapod PSF is used to performhigh-precision, scan-free tracking of multiple emitters over anexceptionally large z-range.

As previously discussed, an imaging model is used by the circuitry. Theimaging model is based on scalar diffraction theory of light from apoint source (i.e. polarization effects are not included), which yieldsimulation results that match experimentally obtained data. For adescription of more detailed modeling considerations, reference may bemade to FIG. 2 which for various example embodiments, can involve animage model (e.g., an image formulation model) built for 3D imagingusing a function, such as:I(u,v;x,y,z)∝|F{E(x′,y′;x,y,z)P(x′,y′)}|²,where I(u, v) is the image, or the intensity in the image plane 232(e.g., camera plane), of a point source located at position (x, y, z) insample space, relative to the focal plane and the optical axis (z). Thefield in the pupil plane, caused by the objective lens 216 (e.g., pointsource), is denoted by E(x′, y′), and F represents the 2D spatialFourier transform with appropriate coordinate scaling. The complexfunction P(x′, y′) is the pattern imposed in the pupil plane by a phasemask 228 (e.g., mask or an SLM).

The optical model consists of a two-layer experimental system consistingof water (refractive index n₁=1.33), and glass/immersion oil (which havematched refractive index of n₂=1.518). Light from a single emitter inthe sample acquires a phase factor (i.e. defocus) determined by thedistance between the emitter and the interface separating layer 1 andlayer 2 (z₂) and the distance between the microscope focal plane and theinterface (z₂). An additional phase factor _(P) is imposed by the phasemask—which, by virtue of the 4 f system, is modeled as being locatedwithin the pupil of the apparatus objective. For a given emitter, theoverall phase ψ_(pupil) of light at a given point {x′, y′} within theapparatus pupil is given by the equation:

${\psi_{total}\left( {x^{\prime},y^{\prime}} \right)} = {{P\left( {x^{\prime},y^{\prime}} \right)}e^{{i\; k\; n_{1}z_{1}\sqrt{1 - x^{\prime 2} - y^{\prime 2}}} + {i\; k\; n_{2}z_{2}\sqrt{1 - {\frac{n_{1}}{n_{2}}{({x^{\prime 2} + y^{\prime 2}})}}}}}}$

Note that if the interface is between the focal plane and the emitter,the sign of z₂ is positive. If the interface is closer to the objectivelens than the focal plane, z₂ is negative. In this expression, acoordinate system is used that is normalized such that points along thecircle √{square root over (x′²+y′²)}=N.A./n₂ lie on the outer edge ofthe tetrapod phase mask. Due to the objective, the electric field oflight along the outer edge of the microscope pupil has a greateramplitude than light close to the center of the pupil. This amplitudefactor A_(pupil) is given by:

${A_{pupil}\left( {x^{\prime},y^{\prime}} \right)} = \left\{ \begin{matrix}\left( \frac{1}{1 - x^{\prime 2} - y^{\prime 2}} \right)^{\frac{1}{4}} & {{{if}\mspace{14mu}\sqrt{x^{\prime 2} + y^{\prime 2}}} \leq {n_{1}/n_{2}}} \\0 & {otherwise}\end{matrix} \right.$

Using the imaging model, the region of non-zero amplitude is limited topoints inside the circle √{square root over (x′²+y′²)}≤n₁/n₂, due to thefact that super-critical light, inhabiting the region n₁/n₂<√{squareroot over (x′²+y′²)}=N.A./n₂ is attenuated for objects (e.g., emitters)which are an appreciable distance (λ<z₁) from the interface. After lighthas propagated beyond the objective, paraxial approximations are valid.Specifically, the tube lens of the microscope performs an opticalFourier transform operation. The electric field present at a point (u,v) in the microscope's image plane, (E_(img)) is given by the formula:E _(img)(u,v)=FT{A_(pupil)(x′,y′)ψ_(pupil)(x′,y′)}=FT{E(x′,y′;x,y,z)P(x′,y′)},where E(x′, y′) is the Fourier-plane electric field mentioned herein inconnection with the image formulation model (equation). The intensitywithin the image plane is then:I _(img)(u,v)=E _(img)(u,v)E* _(img)(u,v).

Finally, object-space coordinates (x, y) are related to image-spacecoordinates (u, v) by a scaling factor M, the overall magnification ofthe microscope.

The precision of a given PSF can be quantified by the Cramer Rao LowerBound (CRLB) which is a mathematical quantity indicative of thesensitivity of a measurement to its underlying parameters. Theoptimization procedure is based on a CRLB minimization method. With theCRLB being related to (e.g., as the inverse of) the Fisher informationmatrix the objective function being minimized is the mean trace of theFisher information matrix (corresponding to mean x, y, z CRLB) over afinite set of N unique z positions in a defined z-range. Morespecifically, the CRLB corresponds to the lowest possible variance inestimating these parameters with an unbiased estimator. In accordancewith various specific embodiments of the present disclosure, themeasurement is a noisy, pixelated manifestation of the PSF (the 2Dimage), and the underlying parameters are the 3D coordinates of theobject (e.g., emitter), as well as the brightness expressed as totalphotons, and a background level. In various embodiments, given theapparatus parameters (such as magnification, numerical aperture,background and signal levels, and a (Poisson) noise model), a numericalimaging model is built based on the above image-model equation and isused to find the Fourier phase pattern P(x′, y′) which yields the PSFwith the lowest theoretical localization variance (or the lowest CRLB).

The objective function being minimized is the mean CRLB in x, y and z,over a predetermined z-range composed of N distinct z (depth) values. Invarious embodiments, the optimization is performed over the set of thefirst 55 Zernike polynomials, so that the sought solution is acoefficient vector c∈ R^(N) with N=55. The mathematical optimizationproblem, solved using Matlab's fmincon function, using the ‘interiorpoint’ method, is therefore:

${\min\limits_{c}{\sum_{{j = \hat{x}},\hat{y},\hat{z}}{\sum_{z \in Z}\sqrt{\frac{1}{I_{j\; j}\left( {c,z} \right)}}}}},$where, assuming additive Poisson noise and a constant background of β,the Fisher information matrix for a point source along the optical axisis given according to the following equation by:

${I\left( {{c;0},0,z} \right)} = {\sum\limits_{k = 1}^{N_{p}}\;{\frac{1}{{\mu_{c,z}(k)} + \beta}\left( \frac{\partial{\mu_{c,z}(k)}}{\partial\theta} \right)^{T}{\left( \frac{\partial{\mu_{c,z}(k)}}{\partial\theta} \right).}}}$Here, θ=(x, y, z) is the 3D position of the emitter, summation isperformed over the sum of image pixels N_(p), and μ_(c,z) is a model ofthe detected PSF for an emitter at z, including the total number ofsignal photons per frame, magnification and pixelation, for a PSFproduced by a Fourier-plane mask P(x′, y′) defined by:P(x′,y′)=circ(r/R)·exp(iD _(zer) ·c)where r=√{square root over (x′²+y′²)}, R is the radius of the pupilplane,

${{{circ}(\eta)} = \begin{Bmatrix}{1,} & {\eta < 1} \\{0,} & {\eta \geq 1}\end{Bmatrix}},$and D_(zer) is the linear operator transforming the vector of Zernikecoefficients to the 2D phase pattern to be projected on the SLM. The SLMis discretized to a 256×256 grid, so that D_(zer) ∈ R²⁵⁶ ² ^(×55), whereeach column is a vector-stacked 2D image of the corresponding Zernikepolynomial.

A set of tetrapod PSFs with z-ranges throughout the 2-20 μm range can bederived by running the optimization procedure iteratively. Starting witha design z-range of 2 μm, the procedure is run once to produce anoptimal PSF. Then, the output solution is used as an initial point foranother iteration, with a larger z-range of 4 μm. This iterative processis repeated, iteratively increasing the z-range by 2 μm each time, to afinal z-range of 20 μm.

Performing optimization with different specified z-ranges, in someembodiments, yields different phase masks (and corresponding PSFs) thatshare common characteristics including for any tested z-range (e.g.,from 2-20 μm), two distinct lobes, with growing transverse distancebetween them as the emitter departs from the apparatus' focal plane. Theorientation of the two lobes of the PSF, in some embodiments, is rotatedby 90° above and below the focal plane. PSFs, in accordance with thepresent disclosure, are therefore referred to as tetrapod PSFs, due tothe 3D tetrahedral shape they trace out as the object is moved in z (theaxial direction).

In accordance with various embodiments, using the above describedimaging apparatus with PSF engineering (e.g. the 4f optical system withphase mask in the Fourier plane), a phase pattern is designed thatproduces different PSFs for different wavelengths. Such embodimentsallow for simultaneous scan-free 3D imaging of objects with differentwavelengths using a signal optical channel (e.g., a single channel). Theresulting phase mask is used to encode spectral information in the PSFof the apparatus. PSF engineering for 3D imaging exploits opticalaberrations for encoding depth and uses chromatic aberrations forencoding color.

In terms of signal compromise, in various embodiments, the elongated PSFused in cell measurement (e.g. FIG. 10A-10C) is around 13% dimmer than astandard PSF. In terms of spectral separation, a liquid crystal SLM insome embodiments generates a multi-wavelength tetrapod PSF at up to a 20um z-range for two objects at wavelengths that are separated by 60 nm ormore. One limitation of the multi-wavelength liquid crystal SLM is themodulated range is limited to around 4π at 633 nm, and has a spectraldependence as the SLM relies on finding the voltage values thatoptimizes the different phase delays for the different wavelengths.Further, the liquid crustal SLM modulates one polarization, which limitsthe detectable signal and degrades object detectability, localizationprecision, and spatial resolution. The limitation of only onepolarization, in various embodiments, is overcome by utilizing theunmodulated part of the emitted light as described above.

In some embodiments, the phase mask is a dielectric mask. A dielectricmask includes a multi-wavelength phase mask that can create a PSF forfive or more different wavelengths, in a 300 nm spectral range.

Various specific embodiments involve a system that includes a 4 foptical processing system with a side-port of an Olympus IX71 microscopeframe, with a 100 times/1.4 NA oil-immersion objective lens. The 4 fsystem includes two 150 nm achromat lenses, a polarizing beamsplitter toreject light polarized perpendicular to the axis along which the phasemask (SLM) is capable of modulating phase, a 512 by 512 pixel SLM, andassorted mirrors for beam-steering. A camera is used to record data. Invarious embodiments, simultaneous illumination of the sample isperformed using a 641 nm diode laser, and a 514 nm line of an Ar-ironlaser. Excitation light is reflected off of a multi-bandpass dichroic,and fluorescence is transmitted through the same dichroic, and passthrough an additional multi-bandpass emission filter, a notch filter,and a 514 long pass filter.

Various blocks, modules or other circuits may be implemented to carryout one or more of the operations and activities described herein and/orshown in the figures. In these contexts, a “block” (also sometimes“circuitry”, “circuit”, or “module”) is a circuit that carries out oneor more of these or related operations/activities (e.g., optimization,encoding wavelength-based characteristics, encoding 3D positions, detectlight, generate 3D image, or manipulate a phase mask). For example, incertain of the above-discussed embodiments, one or more modules arediscrete logic circuits or programmable logic circuits configured andarranged for implementing these operations/activities. In certainembodiments, such a programmable circuit is one or more computercircuits programmed to execute a set (or sets) of instructions (and/orconfiguration data). The instructions (and/or configuration data) can bein the form of firmware or software stored in and accessible from amemory (circuit). As an example, first and second modules include acombination of a CPU hardware-based circuit and a set of instructions inthe form of firmware, where the first module includes a first CPUhardware circuit with one set of instructions and the second moduleincludes a second CPU hardware circuit with another set of instructions.Also, although aspects and features may in some cases be described inindividual figures, it will be appreciated that features from one figureor embodiment can be combined with features of another figure orembodiment even though the combination is not explicitly shown orexplicitly described as a combination.

Terms to exemplify orientation, such as upper/lower, left/right,top/bottom, above/below, and axial/lateral (as well as x, y, and z), maybe used herein to refer to relative positions of elements as shown inthe figures. It should be understood that the terminology is used fornotational convenience only and that in actual use the disclosedstructures may be oriented different from the orientation shown in thefigures. Thus, the terms should not be construed in a limiting manner.

Certain embodiments are directed to a computer program product (e.g.,nonvolatile memory device), which includes a machine orcomputer-readable medium having stored thereon instructions which may beexecuted by a computer (or other electronic device) to perform theseoperations/activities.

Various embodiments are implemented in accordance with the underlyingProvisional Application (Ser. No. 62/146,024) to which benefit isclaimed and which is fully incorporated herein by reference. Forinstance, embodiments herein and/or in the provisional application(including the appendices therein) may be combined in varying degrees(including wholly). Reference may also be made to the experimentalteachings and underlying references provided in the underlyingprovisional application, including the Appendices that form part of theprovisional application. Embodiments discussed in the Appendices are notintended, in any way, to be limiting to the overall technicaldisclosure, or to any part of the claimed invention unless specificallynoted.

The underlying Provisional Application (including its Appendices) arehereby fully incorporated by reference for their general and specificteachings. Appendix A entitled “Precise 3D scan-free multiple-particletracking over large axial ranges with Tetrapod point spread functions”,Appendix B entitled “Precise 3D scan-free multiple-particle trackingover large axial ranges with Tetrapod point spread functions”, AppendixC entitled “Appendix C”, Appendix D entitled “Tetrapod Phase MaskMicroscopy for high precision three-dimensional position estimation overa large, customizable depth range”, and Appendix E entitled “Multi-colorPSF design.” Consistent with embodiments of the present disclosure,Appendices A, B, and D describe and show examples of optical apparatusesand use of the optical apparatuses to localize objects in threedimensions. Appendix C shows examples of localization of objects inthree dimensions using an optical apparatus in accordance with variousembodiments. Appendix E, consistent with embodiments of the presentdisclosure, describes and shows examples of optical apparatus withmulti-color phase masks and use of optical apparatuses to localizemultiple objects in three dimensions and in different wavelengths.

What is claimed is:
 1. An apparatus comprising: a phase mask configured and arranged with optics in an optical path to provide modification of a shape of light simultaneously for each of a plurality of wavelengths of the light concurrently passed from a plurality of objects, wherein the modification is simultaneous for each of the plurality of wavelengths of the light concurrently passed from the plurality of objects, independent of one another and from the optical path; and circuitry configured and arranged to characterize a three-dimensional image of the plurality of objects, that are associated with different colors, based on each of the modified shapes of light and the respective wavelengths that are labeled using different colors.
 2. The apparatus of claim 1, wherein the phase mask is located at a Fourier plane defined by the optical path, and is further configured and arranged with the optics to modify the shape of light for each respective wavelength differently than the shape of light for other ones of the respective wavelengths.
 3. The apparatus of claim 1, wherein the phase mask is configured and arranged with the optics to modify the shape of light for each respective wavelength as the same or similar shape to compensate for different wavelength-dependent characteristics.
 4. The apparatus of claim 1, wherein modifying the shape of light includes redirecting and modifying the light passing along the optical path to create a point-spread function (PSF) at or incident upon an image plane for each respective wavelength.
 5. The apparatus of claim 1, wherein the circuitry is configured and arranged to detect relative movement of different ones of the objects based on each of the modified shapes of light and the respective wavelengths.
 6. The apparatus of claim 1, wherein the phase mask is configured and arranged with the optics to produce different ones of the modified shapes for each respective wavelength by simultaneously providing a different phase delay for each of the respective wavelengths.
 7. The apparatus of claim 1, wherein the phase mask is configured and arranged with the optics to modify the shapes of the light by producing a plurality of point-spread functions (PSFs) for the respective wavelengths of light, the PSF for each respective wavelength being different than the PSF for other ones of the respective wavelengths.
 8. The apparatus of claim 7, wherein the phase mask is configured and arranged with the circuitry to generate an image of a plurality of colors, each of the colors corresponding to one of the wavelengths, on a single optical channel and therein encode the wavelength-based characteristics and information concerning three-dimensional positions.
 9. The apparatus of claim 1, wherein while wavelengths of light passes along an optical path using a phase mask, the phase mask, optical path and circuitry are configured and arranged to provide encoded wavelength-based characteristics in the plurality of wavelengths which correspond to the modified shapes of light.
 10. The apparatus of claim 1, wherein while wavelengths of light passes along the optical path using the phase mask, the phase mask, optical path and circuitry are configured and arranged to: use the phase mask positioned at a Fourier plane to yield a shift-invariant PSF.
 11. A method comprising: providing optics and a phase mask in an optical path; passing light through the optical path to imaging circuitry at an image plane where the light is detectable, and wherein the light is passed from a plurality of objects toward the image plane; and encoding wavelength-based characteristics and information concerning three-dimensional positions of the plurality of objects by modifying a shape of light passing along the optical path for each of a plurality of wavelengths of light passed from the objects.
 12. The method of claim 11, wherein modifying the shape of light includes redirecting and modifying the light, by using the phase mask with the optics, to create a respective point-spread-function (PSF) for each of the respective wavelengths of light passed from the objects via the phase mask, and further including the step of using circuitry to characterize a three-dimensional image of the objects based on each of the modified shapes of the light and the respective wavelengths.
 13. The method of claim 11, wherein modifying the shape of light passing along the optical path for each respective wavelength further includes differently modifying the shape of light to produce different shapes for each respective wavelength by providing a different phase delay for each of the respective wavelengths.
 14. The method of claim 11, wherein modifying the shape of the light for each respective wavelength further includes modifying the shapes of light as the same shape for each respective wavelength by providing a different phase delay for each of the respective wavelengths to compensate for different wavelength-dependent characteristics.
 15. The method of claim 11, wherein encoding wavelength-based characteristics and the three-dimensional positions of the plurality of objects further includes concurrently locating the objects in the single optical path based on the modified shapes of light for each respective wavelength, wherein the modified shapes are independently modified from one another.
 16. The method of claim 15, wherein concurrently locating the objects includes tracking locations of the objects of a plurality of colors, each of the colors corresponding to one of the wavelengths.
 17. The method of claim 11, further including concurrently tracking three-dimensional locations of two or more particles that are labeled using different colors, each of the different colors corresponding to one of the wavelengths, using the encoded wavelength-based characteristics and while light is passing to the phase mask, using the phase mask located at a Fourier plane to yield a shift-invariant PSF.
 18. An apparatus, comprising: an imaging circuit at an image plane in an optical path and configured and arranged to detect light at or incident upon the imaging circuit; optics configured and arranged to pass light from objects toward the image plane; a phase mask configured and arranged with the optics to modify a shape of light passing along the optical path, passed from the objects, wherein the light passing along the optical path is modified to create a point-spread-function (PSF) for each of a plurality of respective wavelengths of light passed from the objects through the optical path; and circuitry configured and arranged to characterize a three-dimensional image of the objects based on each of the modified shapes of light and the respective wavelengths.
 19. The apparatus of claim 18, wherein the circuitry is configured and arranged to generate the three-dimensional image indicative of respective depths of the objects that are at least 3 microns from one another.
 20. The apparatus of claim 18, wherein the phase mask is configured and arranged with the optics to create the PSF for each of the respective wavelengths by laterally shifting the PSF in a direction in the image plane for a first wavelength and laterally shifting the PSF in a different direction for a second wavelength.
 21. The apparatus of claim 18, wherein the wavelengths are separated by at least 60 nanometers from one another.
 22. The apparatus of claim 18, wherein the circuitry is configured and arranged to concurrently characterize a three-dimensional image of two to ten objects that are labeled using different colors, each of the different colors corresponding to one of the wavelengths, using the PSFs.
 23. An apparatus comprising: a phase mask configured and arranged with optics in an optical path to modify a shape of the light for each of a plurality of wavelengths of light passed from a plurality of objects; and circuitry configured and arranged to characterize a three-dimensional image of the plurality of objects based on each of the modified shapes of light and the respective wavelengths, wherein while wavelengths of light passes along an optical path using a phase mask, the phase mask, optical path and circuitry are configured and arranged to: provide encoded wavelength-based characteristics in the plurality of wavelengths which correspond to the modified shapes of light; and simultaneously provide a different phase delay for each of the different wavelengths.
 24. An apparatus comprising: a phase mask configured and arranged with optics in an optical path to modify a shape of the light for each of a plurality of wavelengths of light passed from a plurality of objects; and circuitry configured and arranged to characterize a three-dimensional image of the plurality of objects based on each of the modified shapes of light and the respective wavelengths, wherein while wavelengths of light passes along an optical path using a phase mask, the phase mask, optical path and circuitry are configured and arranged to generate the three-dimensional image of the objects by the light passing along the optical path from the objects to the phase mask and by providing a different phase delay, using the phase mask, for each of the different wavelengths of the light passed.
 25. An apparatus comprising: a phase mask configured and arranged with optics in an optical path to modify a shape of the light for each of a plurality of wavelengths of light passed from a plurality of objects; and circuitry configured and arranged to characterize a three-dimensional image of the plurality of objects based on each of the modified shapes of light and the respective wavelengths, wherein while wavelengths of light passes along an optical path using a phase mask, the phase mask, optical path and circuitry are configured and arranged to: provide encoded wavelength-based characteristics in the plurality of wavelengths which correspond to the modified shapes of light; provide a different phase delay for each of the different wavelengths; and simultaneously encode the wavelength-based characteristics and three-dimensional positions of at least two objects, using a single phase mask and within one field of view, that are labeled using different colors, wherein each of the different colors corresponds to one of the plurality of wavelengths.
 26. An apparatus comprising: optics and a phase mask in an optical path configured and arranged to: pass light through the optical path to an image plane where the light is detectable, wherein the light is passed from a plurality of objects toward the image plane; and encode wavelength-based characteristics and information concerning three-dimensional positions of the plurality of objects by modifying a shape of light passing along the optical path for each of a plurality of wavelengths of light passed from the objects; and circuitry configured and arranged to detect the light at the image plane. 